Structures- Or Why Things Don't Fall Down

by J E Gordon

  The commonest way to guard against Brazier buckling is to stiffen the skin of a thin-walled structure by attaching extra members, such as ribs or stringers, to it. StifFeners which run cir-cumferentially are generally called ‘ribs’, while those which run lengthwise are called ‘stringers’ (except by botanists, who will call them ‘ribs’). The shell-plating of ships is traditionally stiffened by means of ribs and bulkheads, though, recently, large tankers have been built on the ‘Isherwood’ system, which largely depends upon longitudinal stringers. A sophisticated shell structure, such as an aircraft fuselage, is usually stiffened by both ribs and stringers. The hollow stems of grasses and bamboos, which tend to flatten when they are bent, are very elegantly stiffened by means of ‘nodes’ or partitions or bulkheads, spaced at intervals along the stem (Figures 13 and 14).

  Figure 13. Two ways of stiffening a hollow plant stem against local buckling.

  (a) Longitudinal stringers.

  (b) Nodes or bulkheads – common in grasses and bamboos.

  Figure 14. Engineering shell structures such as ships and aircraft generally use both stringers and ribs or bulkheads. This is a diagram of the Isherwood construction often used in oil tankers.

  Leaves, sandwiches and honeycombs

  Thin plates and panels and shells are continually cropping up both in Nature and in technology, and, the larger and the thinner these structures are, the more likely they are to deflect or crumple under bending and compressive loads. In principle, anything which stiffens a column or a panel in bending will also increase its resistance to buckling and so make it stronger in compression. One way of doing this is by staying a strut or a panel with ropes or wires; this is a solution which is never used in plants. Alternatively, and perhaps preferably, one can stiffen the member with ribs or stringers, by corrugating it, or by making it of cellular construction.

  Wood is a cellular material, and so are most other plant tissues, notably the stem-walls of grasses and bamboos. Furthermore, in the competitive struggle for existence, many plants depend critically upon the structural efficiency of their leaves, because they must try to expose the maximum area to sunlight, for photosynthesis, at the minimum metabolic cost. Leaves are therefore important panel structures, and they seem to make use of most of the known structural devices to increase their stiffness in bending. Nearly all leaves are provided with an elaborate rib structure*; the membranes between the ribs are stiffened by being of cellular construction, and in some cases they are further stiffened by corrugations. In addition to all this, the leaf as a whole is stiffened hydrostatically by the osmotic pressure of the sap.

  In engineering structures, panels and shells are very often stiffened by means of ribs or stringers which are glued or riveted or welded to the plating, though this is not always the lightest or the cheapest way of doing the job. Another way of tackling the problem is to make the shell-plating in two separate layers which are then spaced apart by being glued to some kind of continuous support, usually made as light as possible. Arrangements of this kind are called ‘sandwich constructions’.

  In modern times sandwich panels were first used for serious constructional purposes by Mr Edward Bishop, de Havilland’s famous chief designer, for the fuselage of the now-forgotten Comet aircraft of the 193Os.† It is probably best known for its use in the successor to this aeroplane, the war-time Mosquito. In both these aircraft the core of the sandwich was made of light-weight balsa-wood, with skins of heavier and stronger birch plywood glued to either side.

  Though the Mosquito was a most successful aircraft, balsa-wood is apt to soak up water and rot; moreover, supplies of this rather soft and fragile tropical wood are limited in quantity and variable in quality. As things turned out, research on core materials for sandwich shells and panels was much stimulated at about this time by another factor altogether; this was the introduction of airborne radar. With this equipment the moving radar reflector or ‘scanner’ had to be housed and protected by putting it inside a large streamlined dome or fairing, which soon came to be known as a ‘radome’. Naturally these fairings had to be transparent to high-frequency radio waves, and this meant that, in practice, they had to be made from some sort of plastic, usually Fibreglass or Perspex. The transparency of the radome shell to radar could be much improved – at least in theory – by the use of a sandwich construction whose thickness was carefully related to the wavelength of the radiation which was being transmitted – in exactly the same way as the thickness of the coating or ‘blooming’ on a modern camera lens is related to the wavelength of visible light.

  Damp balsa, like any other damp wood, is nearly opaque to radar; and under war-time conditions balsa is practically always damp. This ruled out its use for radomes, and so it was necessary to develop more waterproof light-weight materials. This was done by ‘foaming’ artificial resins of various kinds. The result looked something like a meringue or ‘Aero’ chocolate (Figure 15). A good many foamed resins of this kind were developed; they have a number of virtues, and they were used not only for the cores of radome sandwiches but for all sorts of other structural sandwich panels as well. Some of them are still in use today. They are used, for instance, in boatbuilding because the walls of their cells or cavities are nearly impervious to water. However, for the cores of sandwich panels of the highest structural efficiency, resin foams are rather heavier and rather less stiff than one might wish. In other words, the market for light-weight core materials was more or less an open one.

  Figure 15. Foamed resins are often used as light-weight core materials in sandwich constructions.

  One day, towards the end of 1943, a circus proprietor called George May called to see me at Farnborough. After he had told me several Gerald Durrell-type stories about the difficulties of keeping monkeys in travelling circuses, he produced something which looked like a cross between a book and a concertina. When he pulled on the ends of this invention, the whole thing opened out like one of those coloured-paper festoons which people use for Christmas decorations. It was in fact a sort of paper honeycomb of very light weight but of quite surprising strength and stiffness. Did I think that such a thing could be of any use in aircraft? The snag, as George May modestly admitted, was that, since it was only made from brown paper and ordinary gum, it had no moisture resistance at all and would fall to bits if it got wet.

  This must have been one of the relatively few occasions in history when a group of aircraft engineers have been seriously tempted to throw their collective arms around the neck of a circus proprietor and kiss him. However, we resisted the temptation and told May that there could be no serious difficulty in waterproofing the paper honeycomb by means of a synthetic resin.

  This was exactly what we did (Figure 16). The paper from which the honeycomb was to be made was impregnated before use with a solution of uncured phenolic resin. After the honeycomb had been made and expanded, the resin was cured and hardened by baking it in an oven. As a result the paper was not only made waterproof but also strengthened and stiffened. This material was very successful and was used in the cores of sandwiches for all kinds of military purposes. Though it is not used a great deal in aircraft nowadays, something like half the household doors in the world are made by gluing thin sheets of plywood or plastic on either side of a paper honeycomb. It is even more widely used abroad, especially in America, than in England, and the world production of paper honeycomb must be very considerable.

  Figure 16. Construction and use of paper honeycomb.

  (a) Resin-impregnated paper is printed with parallel stripes of glue.

  (b) Many sheets are glued together into a thick block with glue stripes staggered.

  (c) When the glue is set, the block of material is expanded into a honeycomb. After this the resin is hardened.

  (d) Slabs of honeycomb are glued between sheets of ply, plastic or metal to form a structural sandwich.

  Although the use of sandwich construction, foamed resin cores and honeycombs is relatively new in engineering, it
has been used for a very long time in biology. What is called ‘cancellous’ bone (Figure 17) exploits this principle. Each of us carries around quite a good example in the bones of our skulls, which are, of course, subject to bending and buckling loads.

  Figure 17. Cancellous bone.

  * * *

  * The result may be a concentration of mass so dense that its own gravita tional field is strong enough to prevent, not only the escape of any matter’ but also the departure of all forms of radiation. Thus no two-way communication is possible with such an area, and these regions of the Universe are for ever barred to us. These localities are known as ‘Black Holes’. Like the island in Sir James Barrie’s eerie play Mary Rose, they ‘like to be visited’; but nothing can ever return.

  * In so far as failure in both tension and compression tend to occur by shearing – as in ductile metals – the tensile and compressive strengths would be identical. However, there are so many exceptions to this rule as to make it practically valueless.

  * Note that many seaweeds, which are made largely from alginic acid – a weak and brittle substance – are pre-stressed in the same sense as reinforced concrete. Just as reinforced concrete economizes in steel, so seaweeds economize in the scarce, strong component, cellulose.

  * As a crack or a compression crease with a straight front (like a saw cut) penetrates across a round section its surface area may increase more rapidly than the rate of release of strain energy from the material behind it; and so Griffith is frustrated.

  * Pronounced ‘Oiler’.

  * Except, of course, his increasing blindness in later life.

  * Several modern proofs of Euler’s formula are to be found in the textbooks. See, for instance, The Mechanical Properties of Matter by Sir Alan Cottrell.

  * In a thin-walled circular tube local buckling will generally occur when the stress in the skin reaches a value equivalent to

  where t = wall thickness

  r = radius of tube

  E = Young’s modulus.

  * The ribs of the leaf of the Victoria Regia lily are traditionally supposed to have inspired Sir Joseph Paxton’s design for the Crystal Palace in 1851.

  † Which had no direct connection with the later jet airliner of the same name.

  Part Four

  And the consequence was...

  Chapter 14 The philosophy of design

  –or the shape, the weight and the cost

  Philosophy is nothing but discretion.

  John Selden (1584–1654)

  As we have seen, very much the commonest day-to-day practical use of structural theory is in analysing the behaviour of some specific structure: either one which it is proposed to build, one which is actually in existence but whose safety is in question, or else one which has, rather embarrassingly, already collapsed. In other words, if we know the dimensions of a given structure and the properties of the materials from which it is made, we can at least try to predict how strong it ought to be and how much it will deflect. However, although calculations of this sort are clearly very useful in particular instances, this kind of approach is only of limited help to us when we want to understand why things are the shape they are or when we want to choose which, out of several different classes of structure, would be best for a particular service. For instance, in making an aeroplane or a bridge, would it be better to use a continuous shell structure made from plates or panels or else a criss-cross lattice arrangement built up from rods or tubes and braced, perhaps, with wires? Again, why do we have so many muscles and tendons and comparatively few bones? Furthermore, how is the engineer ever to select from the large variety of materials which are usually available? Should he make his structure from steel or aluminium, from plastic or from wood?

  The ‘design’ of plants and animals and of the traditional artefacts did not just happen. As a rule both the shape and the materials of any structure which has evolved over a long period of time in a competitive world represent an optimization with regard to the loads which it has to carry and to the financial or the metabolic cost. We should like to achieve this sort of optimization in modern technology; but we are not always very good at it.

  It is not widely realized that this subject, which is sometimes called the ‘philosophy of design’, can be studied in a scientific way. This is a pity, because the results are important, both in biology and in engineering. Although not much regarded, the study of the philosophy of design has, in fact, been going on for quite a number of years. The first serious engineering approach to the subject was made by A. G. M. Michell around 1900.* Though biologists had been making remarks about the ‘square-cube law’ (Chapter 9) practically since it was propounded by Galileo, it was not until 1917 that Sir D’Arcy Thompson published his beautiful book On Growth and Form (still in print), which was the first general account of the influence of structural requirements on the shapes of plants and animals. For all its many virtues, the book is not a very numerate one, and the engineering views expressed are not always sound. Though greatly, and justly, praised, Growth and Form did not have much real influence on biological thinking, either in its own time or for long afterwards. It does not seem to have influenced engineers very much either, no doubt because the time for an interaction between biological and engineering thought was not ripe.

  In recent years the chief exponent of the mathematical study of the philosophy of structures has been H. L. Cox. Besides being a distinguished elastician, Mr Cox has the additional merit of being an expert on Beatrix Potter. I hope that he will forgive me for saying that he is in some ways a little like the great Thomas Young. For he shares not only something of Young’s genius, but also a good deal of Young’s obscurity of presentation. I am afraid lesser mortals often find Cox’s expositions difficult to follow without the aid of an evangelist or interpreter. This may account for the fact that his work has received less attention than it deserves. Much of what follows is based on Cox, directly or indirectly. Let us begin with his analysis of tension structures.

  The design of tension structures

  It is a curiosity of engineering design that it is impossible to fashion a simple tension member without first devising some end fitting through which the load may be applied; and whether the material be wrought-iron or liana, wire rope or string, the stress system in the end fitting is a great deal more complicated than simple tension. There is plenty of scope for theory in the design of tension end fittings, but there is also a great deal of experience; and whether the competition is from the ancient pygmies’ mastery of the craft of making knots in lianas, or from Brunei’s development of efficient eye bars, experience will often dictate the design. Still the theorist has the final word.

  H. L. Cox, The Design of Structures of Least Weight (Pergamon, 1965)

  If we did not have to consider the effect of end fittings the philosophy of tension structures would be very simple indeed. For one thing, the weight of a tension structure, fitted to carry a given load, would be proportional to its length. That is to say, a rope strong enough to carry a load of one ton over a distance of one hundred metres would weigh just a hundred times as much as a rope safe to carry the same load over one metre. Furthermore, provided that the load were evenly shared, it would make no difference whether a given load were supported by one single rope or tie-bar, or by two ropes or bars each having half the cross-section.

  This simple view is upset by the necessity for end fittings: that is to say, by the need to get the load in at one end of the member and out at the other. Even an ordinary rope will need a knot or a splice at each end. The knot or splice will be relatively heavy and may cost money. If we are to do an honest reckoning this weight and cost will have to be added to that of the bare tension member itself. The weight and the cost of the end fittings will be just the same, for a given load, whether the rope be long or short. Thus, other things being equal, the weight and cost of a tension member per unit length will be less for a long member than for a short one. In other words the weight is not di
rectly proportional to the length.

  Again, it can be shown, from the algebra and geometry of such a system, that the total weight of the end fittings of two tension bars, operating in parallel, is less than that of the end fittings of a single rope or bar of equivalent cross-section.* It follows that, in general, weight is saved by subdividing a tensile load between two or more tension members instead of carrying it in a single one.

  As Cox points out, the stress distribution in end fittings is always complex and must include more or less severe stress concentrations, from which cracks will spread if they get the chance. Thus both the weight and the cost of the fittings will depend both upon the skill of the designer and also upon the toughness – that is to say, the work of fracture – of the material. The higher the work of fracture, the lighter and the cheaper the fitting will be. However, as we saw in Chapter 5, toughness is likely to diminish as tensile strength increases. In the case of common engineering metals, like steel, the work of fracture falls dramatically with increase of tensile strength.